Parallel Circuit and Impedance

In a parallel circuit, the components are connected in such a way that they have a common voltage across them. This means that the voltage across each component remains the same, while the current through each component can vary. In this type of circuit, the total current is divided among the different branches of the circuit.

Impedance in AC Circuits

Impedance is a concept used in AC circuits to represent the opposition to the flow of current. It is similar to resistance in DC circuits but takes into account both resistance and reactance. Reactance is the opposition to the flow of current caused by inductance or capacitance.

In an AC circuit, the impedance is represented by a complex quantity, consisting of a real part (resistance) and an imaginary part (reactance). Impedance is denoted by the symbol Z and is measured in ohms (Ω). It is given by the formula:

Z = R + jX

Where R is the resistance and X is the reactance.

Parallel Circuit and Admittance

In a parallel circuit, the impedance of each component is connected in parallel with each other. This means that the total impedance of the circuit is the reciprocal of the sum of the reciprocals of the individual impedances. However, when analyzing parallel circuits, it is more convenient to work with admittance instead of impedance.

Admittance is the reciprocal of impedance and is denoted by the symbol Y. It represents the ease with which current can flow through a circuit. Admittance is also a complex quantity, consisting of a real part (conductance) and an imaginary part (susceptance). It is given by the formula:

Y = G + jB

Where G is the conductance and B is the susceptance.

Why Admittance instead of Impedance?

In a parallel circuit, the total current is divided among the different branches of the circuit. When using impedance, the analysis becomes more complex as we have to calculate the individual currents through each component. However, when using admittance, the analysis becomes simpler as we can directly add the admittances of the components.

By considering admittance instead of impedance in a parallel circuit, we can easily calculate the total current flowing through the circuit. This simplifies the analysis and makes it easier to determine the behavior of the circuit. Therefore, in a parallel circuit, we consider admittance instead of impedance.

Capacitance